An Integrated Progressive Hedging and Benders Decomposition with Multiple Master Method to Solve the Brazilian Generation Expansion Problem

TL;DR

This paper introduces an advanced decomposition method combining Benders and Progressive Hedging techniques to efficiently solve large-scale hydrothermal expansion planning problems, demonstrating significant speedups and cost savings using realistic Brazilian power system data.

Contribution

It develops a novel integrated approach with multiple master problems and penalization to accelerate convergence and incorporate nonanticipative operational policies in hydrothermal planning.

Findings

Method is 60% faster than benchmarks.

Cost savings of 7.64% with nonanticipative policies.

Improved spot price profiles and operational efficiency.

Abstract

This paper exploits the decomposition structure of the large-scale hydrothermal generation expansion planning problem with an integrated modified Benders Decomposition and Progressive Hedging approach. We consider detailed and realistic data from the Brazilian power system to represent hourly chronological constraints based on typical days per month and year. Also, we represent the multistage stochastic nature of the optimal hydrothermal operational policy through co-optimized linear decision rules for individual reservoirs. Therefore, we ensure investment decisions compatible with a nonanticipative (implementable) operational policy. To solve the large-scale optimization problem, we propose an improved Benders Decomposition method with multiple instances of the master problem, each of which strengthened by primal cuts and new Benders cuts generated by each master's trial solution. Additionally, our new approach allows using Progressive Hedging penalization terms for accelerating the convergence of the method. We show that our method is 60\% faster than the benchmark. Finally, the consideration of a nonanticipative operational policy can save 7.64\% of the total cost (16.18\% of the investment costs) and significantly improve spot price profiles.